Adams still cautious after his rampant team send records tumbling
Vale bullied and battered an uninspiring Spireites outfit that were made to look more like relegation fodder than genuine promotion contenders.
Striker Marc Richards took the match ball home after hitting his first hat-trick in Vale colours, while goals from Rob Taylor and Craig Davies completed the rout.
It was Vale's biggest win since hammering League One rivals Barnsley 5-0 in April 2005, while it was their biggest away victory since their 6-0 mauling of Fulham in March 1987.
It was also Vthe club's first triumph at Saltergate in nine games, with their last success there – by a 2-1 scoreline – coming in April, 1989.
More importantly, Vale leapfrog two places to ninth in League Two, leaving them a tantalising three points adrift of the play-off zone.
Manager Micky Adams, however, is determined to keep his feet on the ground.
"We're not good enough for the play-offs," said a cautious Adams as he turned his attention to Saturday's trip to lowly Cheltenham.
"This result means if we get everything right, we can beat anybody.
"We've got teams to play in the top half of the table and we'll play a major part in who goes up and who doesn't.
"We hope this gives us a platform to build on and we'll see how far we can go. But we have to apply ourselves the best we can.
"We know the potential is there and we go to Cheltenham full of confidence."
Unconvinced by Adams's clever game of bluff in the wake of such a sensational victory, the persistent pack of press hounds at least got him to admit: "What I think and what I tell you people are probably two different things.
"I wouldn't rule us out of it, but we've still got a lot to do."
Having sat in mid-table for most of the season, Vale have at last moved on to the shoulders of the top seven sides and look well-placed to gatecrash the play-off party in May.
Now they must build on securing back-to-back league victories for only the third time this season following last Tuesday's 2-1 home victory over Bradford City.
While fifth-placed Chesterfield produced a powder puff display, that should not take anything away from Vale's powerhouse performance against a team that had won seven of their previous nine games.
The angry home supporters chanted 'what a load of rubbish' at the final whistle.
But Richards's treble was of the highest quality. Rob Taylor had already given the visitors the lead before Richards grabbed his first goal in the 43rd minute, when Davies flicked on a long punt up-field by keeper Joe Anyon.
The ball dropped to Richards on the edge of the six-yard box, where the 27-year-old swivelled to angle his shot into the far right-hand corner.
Six minutes after the break, Richards almost broke the goal frame with a rasping drive after collecting the ball on the left.
The striker drove inside before crashing a bullet of a shot against the underside of the bar and into the net from a slight angle.
He completed his hat-trick on 79 minutes by heading Lee Collins's measured right-flank centre into the roof of the net from seven yards.
Richards, who was a target of the boo boys earlier in the season, was treated to a rousing reception from the 670-strong travelling support when he was withdrawn in the 82nd minute.
"We believe in Marc and he believes in the way we play," said Adams.
"He's a big part of our group because he's a leader and I'm delighted for him.
"I've never seen home fans clapping off an opposition centre-forward – that tells its own story."
At the other end, Anyon was barely troubled nearly 12 months after suffering a broken leg during Vale's 2-1 defeat at Saltergate on March 28 last season.
Adams made just one change to the side that defeated Bradford, with right-back Adam Yates dropping to the bench after recovering from a groin injury.
Meanwhile, left-back Kris Taylor earned a recall while Collins took care of defensive duties on the opposite flank.
Vale started well as Davies met a low right-flank delivery from Richards with a clever flick that flashed wide, before Spireites keeper Tommy Lee bravely kept out Rob Taylor's close-range effort.
But there was nothing Lee could do about Taylor's 19th-minute strike.
The 25-year-old surged forward from deep and from the edge of the area guided a precise low shot inside the left-hand post to claim his ninth goal of the campaign.
While the hosts were limited to a few half chances, Davies and winger Lewis Haldane missed the target with headers.
But Vale were given an almighty scare in the 42nd minute when Chesterfield midfielder Adam Rundle connected with Drew Talbot's right-wing cross at the far post, only to horribly slice his six-yarder wide.
Richards's two-goal burst either side of half-time sapped the life out of Chesterfield before the striker claimed his hat-trick and Davies completed the scoring from the penalty spot.
After springing the offside trap, Davies raced clear in the 85th minute before being hauled down by Alan Goodall who was red-carded for a professional foul.
With Richards, Vale's regular penalty taker, watching on from the sidelines, Davies took responsibility from 12 yards and duly lashed the ball into the bottom left-hand corner.
"We came here expecting to win – we were nice and positive and sent out a positive team," said Adams.
"If you look at our recent performances, somebody was going to get a spanking.
"We have gained a little bit of confidence and every member of the squad played their part – it was fantastic."
